FX Digital Option

ORE defines the product as follows:

A Digital FX Option is an option whose payout is either zero or a fixed predetermined amount (Cash-or-Nothing). Payout depends on whether the underlying FX spot rate expires in-the-money at the expiration date.

Source: ORE User Guide, Products catalogue, fx_digitaloption.tex.

ORE adds that digital FX options have European exercise with payout at expiry. The buyer of a digital FX option pays a premium to the seller.

An FX digital option is a bet on one outcome. If the rate settles on the right side of the strike, the payout is fixed. If not, the payout is zero. There is no middle ground. The fixed payout makes the value easy to read as a probability.

The FxDigitalOptionData node includes one OptionData node plus elements specific to the option. The Strike sets the boundary. The PayoffAmount and PayoffCurrency set the fixed payout. ForeignCurrency and DomesticCurrency name the rate. The call pays when the rate at expiry sits above the strike. The put pays when it sits below.

A digital option equals the limit of a call spread as the two strikes converge. Its value is the discounted probability that the rate ends on the right side of the strike. Volatility changes the value through the probability, not through the payoff size. The payoff amount is fixed, so the option has no linear payoff tail.

• The FX spot rate. Its position against the strike sets the odds.
• The volatility of the pair. It spreads the terminal rate around the forward.
• The interest rates in both currencies.
• The strike, the payoff amount, and the payoff currency.

A digital near the strike is volatile to spot. Its delta is highest at the money. Away from the strike the value saturates near zero or near the full payoff.

The option loses time value as expiry approaches. At the money, the value converges to a coin flip on the payoff. In the money, it converges toward the full payoff. Out of the money, it decays to zero. At expiry the payout is decided by the fixing and settles.

A customer who wants a fixed payout on a rate view buys a digital. The payout is known in advance, which suits structured products. Dealers use digitals to shape option books. In ORE Studio a customer books FX digital options to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long European digital call:

<FxDigitalOptionData>
  <OptionData>
    <LongShort>Long</LongShort>
    <OptionType>Call</OptionType>
    <Style>European</Style>
    <ExerciseDates>
      <ExerciseDate>2021-12-14</ExerciseDate>
    </ExerciseDates>
    ...
  </OptionData>
  <Strike>1.1</Strike>
  <PayoffCurrency>USD</PayoffCurrency>
  <PayoffAmount>100000</PayoffAmount>
  <ForeignCurrency>EUR</ForeignCurrency>
  <DomesticCurrency>USD</DomesticCurrency>
</FxDigitalOptionData>

Source: ORE User Guide, Products catalogue, fx_digitaloption.tex, listing FX Digital Option data (optional elements omitted).